I have Sphere with radius R. Inside the sphere I have Two circle. One circle is fixed defined by $\alpha$. Another circle can rotate and the orientation of that circle can be defined by $\beta$. From the centre of the sphere until the edge of the movable circle create $\alpha$ angle with $z$ axis. $h$ and $a$ are distance from the origin and base radius of this circle .
Now when both circle intersect each other what will be the surface area of intersection? Using spherical coordinate system $r,\theta,\phi$, I know that my $\theta $ limit goes from $\gamma$ to $\alpha$. But I am not getting the limit for $\phi$ with this given parameters. I am trying to calculate the intersected surface area using only calculus and trigonometry for relevancy of my future problem.